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A003642 Number of genera of imaginary quadratic field with discriminant -k, k = A191483(n).
(Formerly M0211)
3

%I M0211

%S 1,1,2,2,2,2,2,2,4,2,2,2,4,4,2,2,2,2,4,2,2,4,2,2,2,4,4,4,4,2,2,4,4,2,

%T 4,2,2,4,2,2,2,4,8,2,2,4,2,4,2,2,4,4,4,2,2,4,4,2,4,2,2,4,2,2,4,8,2,4,

%U 2,4,4,2,2,4,4,4,4,2,2,2,4,2,4,2,4,8,4,2,4,2,4,4,2,2,4,2,4,4,2,4,4,4,2,2,4

%N Number of genera of imaginary quadratic field with discriminant -k, k = A191483(n).

%D D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%F a(n) = 2^(omega(A191483(n)) - 1). - _Jianing Song_, Jul 24 2018

%t 2^(PrimeNu[Select[Range[1000], Mod[#, 4] == 0 && SquareFreeQ[#/4] && Mod[#, 16] != 12&]] - 1) (* _Jean-Fran├žois Alcover_, Jul 25 2019, after _Andrew Howroyd_ in A191483 *)

%o (PARI) for(n=1, 1000, if(isfundamental(-n) && n%2==0, print1(2^(omega(n) - 1), ", "))) \\ _Andrew Howroyd_, Jul 24 2018

%Y Cf. A001221 (omega), A003640, A003641, A191483.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, _Mira Bernstein_

%E Name clarified by _Jianing Song_, Jul 24 2018

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Last modified January 24 16:44 EST 2020. Contains 331209 sequences. (Running on oeis4.)